Problems with vector questions

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In summary, the conversation discusses expressing three vectors (a, b, c) in terms of other three vectors (alpha, beta, gamma) and showing that a dot product with the cross product of b and c is equal to a constant (lambda) times the dot product of alpha with the cross product of beta and gamma. The method for finding lambda is also discussed, as well as a question about expressing the Greek-letter vectors in terms of the Latin-letter vectors.
  • #1
aaron27
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Three vectors are expressed in terms of other three vectors
in the form of

a=a1α + a2β + a3γ
b=b1α + b2β + b3γ
c=c1α + c2β + c3γ

How to show that a.(bxc) = λ α.(βxγ) and find out λ?

I knew the first part where we carry out dot and product rule for vectors a.(bxc),
but the other side of the equation I have no idea how to start with.
Anyone knows how to do this?
Thanks.
 
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  • #2
Can you express each of the greek-letter vectors in terms of the latin-letter vectors?
 
  • #3
a=a1(alpha) + a2(beta) + a3(gamma)
b=b1(alpha) + b2(beta) + b3(gamma)
c=c1(alpha) + c2(beta) + c3(gamma)

How to show that a.(bxc) = λ (alpha) .(beta x gamma) and find out λ?
 
  • #4
##\alpha = f(a,b,c)##
##\beta = g(a,b,c)##
##\gamma = h(a,b,c)##

what are f g and h?
 

1. What are vector problems?

Vector problems are mathematical problems that involve the use of vectors, which are quantities that have both magnitude and direction.

2. What are some common types of vector problems?

Some common types of vector problems include finding the resultant vector, determining the magnitude and direction of a vector, and solving for vector components.

3. How are vector problems solved?

Vector problems can be solved using various mathematical techniques such as vector addition, subtraction, and multiplication. Graphical methods, such as vector diagrams, can also be used to solve vector problems.

4. What are some real-life applications of vector problems?

Vector problems have various real-life applications, including physics, engineering, navigation, and computer graphics. They are used to model and solve problems involving forces, velocities, and directions.

5. What are some common mistakes made when solving vector problems?

Some common mistakes made when solving vector problems include forgetting to account for direction, using the wrong formula, and not properly converting between units. It is important to carefully read and understand the problem and double-check calculations to avoid these mistakes.

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